Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The book is motivated by the idea that a full treatment of a variational problem in function spaces would not be complete without a discussion of inﬁnite-dimensional analysis, proper discretization, and the relationship between the two.

The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the BlackÐScholes model.

AudienceThis book is for researchers in optimization and control theory, numerical PDEs, and applied analysis. It will also be of interest to advanced graduate students in applied analysis and PDE optimization.

About the AuthorsKazufumi Ito is a Professor in the Department of Mathematics and an affiliate of the Center for Research in Scientific Computation at North Carolina State University. An internationally recognized expert on control theory, optimization, and inverse problems, Ito has been involved in developing efficient numerical methods for PDEs and variational and interface problems. He was co-recipient of the SIAM Outstanding Paper Award in 2006.

Karl Kunisch is a Professor at the Institute of Mathematics at the University of Graz, Austria. He has held long-term positions at the Technical University of Graz and the Technical University of Berlin and has had visiting positions at Brown University, University of Oklahoma, University of Paris-Dauphine and INRIA Paris - Rocquencourt. His main fields of interest include calculus of variations, optimal control and inverse problems for partial differential equations. He serves on the editorial boards of several journals, including SIAM Journal on Control and Optimization and SIAM Journal on Numerical Analysis, and was co-recipient of the SIAM Outstanding Paper Award in 2006.